Table Of ContentM
ultivariable and
v c
ector alculus
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M
ultivariable and
v c
ector alculus
An Introduction
Second Edition
s M. M , P d
arhan usa h
MERCURY LEARNING AND INFORMATION
Dulles, Virginia
Boston, Massachusetts
New Delhi
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Publisher: David Pallai
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S. M. Musa. Multivariable and Vector Calculus: An Introduction, Second Edition.
ISBN: 978-1-68392-919-2
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Dedicated to my late father Mahmoud,
my mother Fatmeh, and my wife Lama
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C
ontents
Preface xiii
Acknowledgments xv
CHAPTER 1: VECTORS AND PARAMETRIC
CURVES 1
1.1 Points and Vectors on the Plane 1
Exercises 1.1 13
1.2 Scalar Product on the Plane 17
Exercises 1.2 25
1.3 Linear Independence 28
Exercises 1.3 31
1.4 Geometric Transformations in Two Dimensions 34
Exercises 1.4 42
1.5 Determinants in Two Dimensions 44
Exercises 1.5 51
1.6 Parametric Curves on the Plane 53
Exercises 1.6 67
1.7 Vectors in Space 70
Exercises 1.7 84
1.8 Cross Product 87
Exercises 1.8 96
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viii • Contents
1.9 Matrices in Three Dimensions 98
Exercises 1.9 102
1.10 Determinants in Three Dimensions 104
Exercises 1.10 109
1.11 Some Solid Geometry 111
Exercises 1.11 116
1.12 Cavalieri and the Pappus–Guldin Rules 117
Exercises 1.12 120
1.13 Dihedral Angles and Platonic Solids 121
Exercises 1.13 126
1.14 Spherical Trigonometry 127
Exercises 1.14 132
1.15 Canonical Surfaces 133
Exercises 1.15 145
1.16 Parametric Curves in Space 146
Exercises 1.16 151
1.17 Multidimensional Vectors 152
Exercises 1.17 160
CHAPTER 2: DIFFERENTIATION 163
2.1 Some Topology 163
Exercises 2.1 166
2.2 Multivariable Functions 169
Exercises 2.2 174
2.3 Limits and Continuity 176
Exercises 2.3 187
2.4 Definition of the Derivative 189
Exercises 2.4 193
2.5 The Jacobi Matrix 193
Exercises 2.5 205
2.6 Gradients and Directional Derivatives 207
Exercises 2.6 216
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